%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-09-13 19:51:36
 % @LastEditTime: 2021-09-18 16:46:18

 % input:
 % rho: density cell with size of [nele_ma ,1], nele_ma = nelx * nely
 % lx: the length of the coarse element
 % D0 & D1: the elastic tensors of two materials
 
 % output:
 % harm_u is the harmonic solutions for the optimization of NH
%--------------------------
function harm_u = prepare_h(rho, lx, D0, D1)

    %% init
    nele_ma = length(rho(:));
    microx = size(rho{1}, 1);
%     nele_mi = microx^2;

    dx = lx / microx;
    opt_PBC = 0; % opt_PBC is 1 => adopts PBC conditions, 0 => adopts second-order conditions
    
    harm_u = cell(nele_ma,1); % [nnodes, 6 or 9]

    optKE = 2;
    ke0 = intKE(dx/2, dx/2, D0, optKE);
    ke1 = intKE(dx/2, dx/2, D1, optKE);
    [iK_mi, jK_mi, edofMat_mi, ~] = forAssemble(microx, microx);

    %% boundary conditions
    if opt_PBC == 1
        [wfixed, ufixed,d1,d2,d3,d4] = microPBC(microx, microx, lx, lx);  
    else
        [coorx_nodes,coory_nodes] = meshgrid(-lx/2:dx:lx/2, -lx/2:dx:lx/2);
        coory_nodes = flipud(coory_nodes);
        [ufixed, fixeddofs_mi, freedofs_mi] = microQBC(microx, microx, coorx_nodes, coory_nodes);
    end

    %% computation

    optBodyF = 1; % 'zero';
    % optBodyF = 2; % 'effectivity';
    % optBodyF = 3; % 'point-wise';

    for ele_ma = 1:nele_ma
        material = rho{ele_ma}; 

        if opt_PBC == 1 
            harm_u{ele_ma} = microFEAsimp(microx, microx, iK_mi, jK_mi, d1, d2, d3, d4, ufixed, wfixed, ...
                material, ke0, ke1);
        else                                        
            harm_u{ele_ma} = microFEA_QBC_2mat(D0, D1, ke0, ke1, iK_mi, jK_mi, edofMat_mi, dx, dx, ...
                optBodyF, ufixed, freedofs_mi, fixeddofs_mi, material, coorx_nodes, coory_nodes);
        end
    end
end